Mesopotamian Counting Tokens
(Basic counting tokens, c. 4000 BCE)
Archeological digs in the Middle East have uncovered small clay objects with markings on the various faces and edges. Many archeologists and historians have tried to determine the possible use of these tokens in the past century or so. Some thought they were children’s toys or pieces of amateur art. Recent studies have determined these tokens to have been a vital part of the economy as they represented numerical values of a specific commodity. Art historian Denise Schmandt-Besserat is credited with finding the true purpose of the Mesopotamian clay tokens. She discovered six distinct token shapes that represented different measurements of items like grain. Early tokens were spheres, cones, disks, and other basic shapes. These tokens were used by the peoples of Mesopotamia as far back as 7500 BCE. Over time the complexity and uses of the tokens evolved. There began to be writing on the tokens, possibly markings to denote an association to an accurate counting system. By 3500 BCE the tokens began to be used alongside sphere like objects with small pockets meant for the tokens. Many historians believe these spheres were sent alongside goods as an early attempt at a trading invoice.
(Tokens and Envelope, c. 3300 BCE)
The tokens were present in civilizations that didn’t have an established writing system. These tokens predated writing and numerical systems that developed in the same region. Schmandt-Besserat and other historians believe the tokens helped to emphasize the importance of numbering systems and caused the Sumerians to develop the more complex sexagesimal number system present in third millennium Sumer. Tokens and clay envelopes changed in Sumer to represent more than just one of a specific object. Certain tokens would represent ten or sixty portions as opposed to the early system that used one token for one item. There is also a direct link between the tokens and the early development of agriculture. Hunter gatherer groups didn’t have a need for the tokens because they used a simple system of economics, like for like trading. Agriculture brought new economic opportunities and with it the need for a system to manage a more complex economic system. These basic tokens were the beginnings of counting in Mesopotamia and heavily influenced the later development of more modern counting systems.
Frank Swetz. “Mathematical Treasure: Mesopotamian Counting Tokens.” Convergence 10 (2013). Accessed March 8, 2015. http://www.maa.org/publications/periodicals/convergence/mathematical-treasure-mesopotamian-accounting-tokens.
Denise Schmandt-Besserat . “Tokens: Their Significance For the Origin of Counting and Writing.” Denise Schmandt-Besserat. Accessed March 8, 2015. http://sites.utexas.edu/dsb/tokens/tokens/.
Wikipedia contributors, “Sexagesimal,” Wikipedia, The Free Encyclopedia, http://en.wikipedia.org/w/index.php?title=Sexagesimal&oldid=643765109 (accessed March 8, 2015).